Given:
Length of the ladder = 20 ft
Distance between base of the ladder and wall = 4 ft
To find:
The angle measure of the ladder to the ground to the nearest degree.
Solution:
Ladder is the hypotenuse of a right triangle. Here, we have,
Hypotenuse = 20 ft
Base = 4 ft
In a right angle triangle,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\cos \theta=\dfrac{4}{20}[/tex]
[tex]\cos \theta=\dfrac{1}{5}[/tex]
Taking cos inverse on both sides, we get
[tex] \theta=\cos^{-1}\dfrac{1}{5}[/tex]
[tex] \theta=78.46304^\circ[/tex]
[tex] \theta\approx 78^\circ[/tex]
Therefore, the correct option is A.
